Stabilizing the frequency of femtosecond Ti:sapphire comb laser by a

Appl. Phys. B 92, 13–18 (2008)

Applied Physics B

DOI: 10.1007/s00340-008-3058-7

Lasers and Optics

Stabilizing the frequency of femtosecond Ti:sapphire comb laser by a novel scheme

w.-y. chengu t.-h. wu s.-w. huang s.-y. lin c.-m. wu

IAMS, Institute of Atomic and Molecular Science, Academia Sinica, Taiwan, R.O.C.

Received: 31 March 2008/Revised version: 22 April 2008 Published online: 12 June 2008 • © Springer-Verlag 2008

We demonstrated a novel scheme for scanning the absolute frequencies of a femtosecond Kerr-lens mode-locked Ti:sapphire laser with the repetition rate unaffected, where the carrier-envelop phase of the pulse was controlled by slightly shifting pump beam and the repetition rate was phase locked to a stable radio-frequency oscillator. Since it was the first time to stabilize the frequency of a mode-locked laser by referring directly to the frequency of cesium two-photon-transition (TPT) stabilized diode laser, we evaluated the frequency instability and the frequency accuracy that showed the characteristic of being a comb laser. The feature of the comb laser in this report will be significant for multi-photon spectroscopy where the frequency difference between comb lines plays a key role.

ABSTRACT

PACS 06.30.+v;

1

42.60.By

Introduction

Femtosecond mode-locked lasers, also called “optical frequency comb lasers” whenever their absolute frequencies were stabilized, have recently been shown to be novel light sources in the aspect of light–matter interaction. For instance, scientists have used frequency-stabilized modelocked lasers to demonstrate quantum interference [1], control atomic excited state population [2] and perform wide-band high-resolution molecular spectroscopy [3, 4]. In the past, people stabilized the absolute frequencies of mode-locked lasers by the scheme of so-called “self-reference” [5, 6], or by the scheme of referring to wavelength standard lasers [7, 8], in that spectrum expansion by mode-locked lasers or stepwise phase-locking by frequency chain were usually required. In this paper we showed, by evaluating the frequency accuracy, that the frequency of atomic cesium 6s → 8s two-photon transition (TPT) stabilized diode laser could be a good frequency reference of Ti:sapphire comb laser; neither microstructure fiber nor a frequency chain was needed. The absolute comb frequency locking was realized by controlling the horizontal shift of the pump beam and the repetition rate was phase-locked to a stable radio frequency. The advantage of this approach is that orthogonal control between repetiu Fax: +886-2-23624944, E-mail: [email protected]

tion rate ( f rep ) and absolute frequency ( f n ) could be easily reached, which benefits for the experiments of multi-photon spectroscopy where repetition rate plays key role, such as the phenomenon of coherent population trapping (CPT). Furthermore, the approach of the shifting pump beam enlarges the frequency capture range to one order of magnitude comparing with that by varying the pump power [9, 10]. Our approach on building up the comb laser can spare more than 99% available comb laser power for applications since only 3 mW comb laser power was needed for the absolute frequency locking. This is particularly advantageous for some experiments, such as nonlinear laser spectroscopy [1, 11, 12] by comb laser, that needs higher comb laser power. however, it was known that comb laser frequencies were very sensitive to the variation of repetition rate ( f rep ) whereas the f rep drift was inevitable. We overcome this problem by designing a particular cooling base and the free drift of frep was successfully controlled within 50 Hz so that the general problem of long-tern f rep -drift of Ti:sapphire laser systems was resolved. In terms of direct frequency locking, other researchers have directly locked the frequency of a mode-locked Ti:sapphire laser against a wide-band coating Fabry–P´erot cavity [13]. However, reliable atomic or molecular references were always needed to ensure the reproducibility of absolute frequencies. Hence, we chose a narrow resonance of atomic cesium 6S1/2 → 8S1/2 ( F = 3 → F = 3) hyperfine transition (TPT, 822 nm) as the reliable reference of our pulse laser. The advantages are; 1. The transition frequency has been determined [11]. 2. The corresponding diode laser (822 nm) is commercially available that adds the flexibility to integrate this frequency reference laser into optical systems. 3. The transition wavelength is within the gain center of Ti:sapphire laser emission spectrum. Therefore, neither expanding comb laser spectrum nor setting up frequency chain is needed to lock pulse frequencies. 4. The S → S hyperfine transitions are free from linear Zeeman shift that keeps comb frequencies in good reproducibility. 5. The corresponding hyperfine transitions ( F = 3 → F = 3 and F = 4 → F = 4), with their high spectral separation (> 4 GHz), could be easily identified by a commercial wave meter.

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Applied Physics B – Lasers and Optics

2

Setup

2.1

Outlook

Figure 1 is the block diagram of our experimental setup. The reliable frequency reference of pulse laser was provided by a cesium two-photon stabilized (CTS) diode laser system, with a 4.4 × 10−13 (∆ f = 160 Hz at 60 s) frequency instability [14]. The double-pass acoustic-optical modulator (DPA) is for modulating laser frequency to retrieve the cesium TPT hyperfine spectrum, and for linearly scanning the absolute frequency of pulse laser that will be mentioned in details in Sect. 2.3. A stray light from the wedged output coupler of a Kerr-lens mode-locked (KLML) laser was used for detecting the repetition rate ( f ceo ), as indicated in Figs. 1 and 2. The repetition rate ( f rep ) was then phase locked against an Agilent 8644A synthesizer (S1) with an 8 mHz instability at 0.2 s. The absolute frequency of the n -th mode ( f n ) was found by beating f n against the aforementioned CTS diode laser, and was stabilized by phase locking the beat note against the other Agilent 8644A synthesizer (S2). All the instruments’ time bases in Fig. 1 were phase locked to a universal standard via the global position satellite (GPS) system to provide their long-term frequency accuracy. Under 4.8 W pump power at 532 nm, the maximum output power of the KLML laser was 440 mW at 820 ± 20 nm and 250 mW at 850 ± 20 nm, with 25 fs pulse width. As Fig. 1 shows, an notch-coated mir-

ror at 820 ± 5 nm was employed immediately after laser output, with a small tilt angle, for conducting most of the laser power to the user while leaking out the 822 nm laser modes (∼ 3 mW) for the f n -stabilization. When pulse dispersion was considered, particularly for the experiments concerning the time-domain peak power [12], the notch-coated mirror was inadequate and could be replaced by one 90% reflectance laser output coupler (OC) with small tilt angle. The resultant weakly chirped 29 fs pulse is presented in the dash-line inset of Fig. 1, showing insignificant attrition of pulse peak power. 2.2

Frequency stabilization

The KLML laser in Fig. 1 was a z -type Ti:sapphire laser [15], which was modified from a commercially available model [16], as depicted in Fig. 2. All the mirror mounts were replaced by high stable mirror mounts [17] and the Ti:sapphire crystal (XTAL) was temperature controlled to within 0.01 ◦ C variation by a pair of TE coolers to quietly dissipate the crystal heat. The repetition rate ( f rep ) could be long-range tuned from 80 to 100 MHz by moving the outputcoupler (OC) with a translational stage (TS), and could be finely tuned within several mHz by controlling the position of a piezo-mounted end mirror (EM, PZT1). The absolute frequency ( f n ) of one certain mode of KLML could be longrange (45 MHz) scanned as well as be stabilized by horizon-

FIGURE 1 The block diagram of our frequencystabilized Kerr-lens mode-locked laser system. KLML – Kerr-lens mode-locked femtosecond laser; S1,2 – frequency synthesizer 1,2; CTS – cesium two photonstabilized; AOM – acousto-optic modulator; OI – optical isolator; DPA – double pass AOM; GPS – global position satellite; FL – feedback loop; f rep : repetition rate; NM – 822 nm notch-coated mirror; OC – 90% reflectance output coupler; this component is optional in the case of minimmal pulse dispersion being required; APD – avalanche photo-diode; PL – pump laser; τau – measured by interferometric autocorrelator; τp – deduced pulse intensity width (sech2 (t) fit). The cesium spectrum was retrieved from DPA frequency dither, see text

CHENG et al.


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FIGURE 2 Block diagram for controlling the absolute frequency of our mode-locked laser. The scales are not proportional to the real situation. XTAL – Ti:sapphire crystal; OC – output coupler; TS – translational stage; EM – end-mirror; PL – 532 nm pump laser; PZT1,2 – piezo-electric transducer; Grey line stands for pump beam and black line stands for laser beam in cavity. Right part are Allan deviations recorded from the frequency counter 2 of Fig. 1; “PZT2 only” means that f n was stabilized by PZT2 only; “AOM + PZT2” means that f n was stabilized by both AOM and PZT2 with different loop transfer functions, respectively

tally shifting the pump beam using PZT2, with 0.0014 µm/V displacement. Since the voltage applied on PZT2 never exceeded 500 V, the maximum output beam shifting of the Ti:sapphire laser was estimated as being around 0.5 µm. This approach provides excellent orthogonal control between f rep stabilization and f n -stabilization. For investigating the orthogonality, we scanned fn over a half repetition rate by PZT2 and monitored the frequency fluctuation of the stabilized f rep by frequency counter 1 in Fig. 1; no obvious interlock was found within 8 mHz uncertainty (at 0.2 s gate time). Moreover, comparing with the approach of controlling the pump power [9, 10] where the capture range of f n -locking was around 2 MHz in our laser system, the approach of shifting pump beam provides one order of magnitude better capture range (35 MHz) thus frequency locking could routinely last for several hours. The principle of the orthogonal control could be comprehended by analyzing the variation of the repetition rate ( f rep ). In other words, when we horizontally shifted the pump beam, a slight mode mismatching modified the self-phase modulation which was pulse-intensity-related, and that changed the round-trip carrier-envelop phase; while the change of repetition rate was not obvious for Vg c dn f rep = = /(L 0 + S(cot ϕ − cot θ) Lc n + ωc dω ωc − Dn 2 (I0 − I )) ,

(1)

where Vg is the average group velocity inside the cavity [10]; S (≥ 0) stands for the horizontal displacement of pump beam; L c is the optical cavity length that equals to L 0 + S(cot ϕ − cot θ) − Dn 2 (I0 − I ) where D is the XTAL length and ϕ, θ

are indicated in Fig. 2; n = n 0 + n 2 I is the average nonlinear index; I0 is the laser intensity inside the cavity when PZT2 was not activated ( S = 0) and I is that varied with S, that is, I ≡ I0 − βS; Since ( dn 2 Dω) is relatively small (∼ 10−38 ) [10], (1) could be approximated as vg c/(n 0 + n 2 I ) c/(n 0 + n 2 I0 − βSn 2 ) ∼ ∼ Lc L 0 + αS (L 0 + αS) c , ∼ (n 0 + n 2 I0 )L 0 + α n 0 + n 2 I0 − βn 2 L 0 S

f rep =

(2)

where n 0 denotes (n 0 + ωc ( dn 0 / dω))average ; α ≡ (cot ϕ − cot θ)Dn 2 β . Since S L 0 and the value of α in our laser system could be adjusted so that |α(n 0 + n 2 I0 ) − βn 2 L 0 | 1, (2) is approximated as f rep =

c ∼ const . (n 0 + n 2 I0 )L 0

The physical meaning is interpreted as follows. When mode mismatching is performed ( S = 0), n 0 + n 2 I in (2) will decrease since I decreases. That is, Vg increases. Meanwhile, L c (= L 0 + αS) increases so that compensates for most of the changing in frep . The right part of Fig. 2 presents the Allan deviations recorded from frequency counter 2 as in Fig. 1. When PZT2 was fed back only, the right upper panel of Fig. 2 shows 1 kHz instability at 1000 s sampling times. If the high frequency component of the error signal was further fed back to the AOM with different loop transfer function [18], one order of magnitude improvement could be achieved as shown in the bottom right of Fig. 2. Therefore, with PZT2 enlarging the frequency capture range and AOM for further stabilization, our

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Applied Physics B – Lasers and Optics

(a) Particular-designed cooling base which was installed beneath the comb laser. (b) The repetition-rate drifted 18 kHz during a 13 h period (upper panel), and was reduced two orders of magnitude after installing the cooling base (lower panel)

FIGURE 3

comb frequencies are easy to scan and stabilize. This fact also implies that people may use just one high frequency response component, such as the electric-optical modulator (EOM), to perform the beam shifting. The fceo of our comb laser hence could be deduced from the fixed f rep and the fixed f n for f ceo = f n − n × f rep .

per panel shows repetition rate over time in which no cooling base was installed; we recorded 18 kHz drift of repetition rate during 800 min (∼ 13 h, extrapolated). When we installed the cooling base, a great improvement (two orders of magnitude) was achieved as shown in the bottom panel of Fig. 3b. The long term drift of repetition rate never exceed 50 Hz that was always within the capture range of PZT1.

(3) 2.3

Note that there are essential differences between the schematic of f n -stabilization (in this paper) and fceo -stabilization (in the 1 f –2 f interferometer scheme). However, in the scheme of f n -stabilization, the individual frequency fm of the modelocked laser was determined by (m − n) × f rep + f n while in the scheme of f ceo -stabilization, f m was determined by m × f rep + f ceo . Since m − n could be much smaller than m , the absolute frequency of f m in our f n -stabilization scheme was less sensitive to the fluctuations of frep , although f ceo in the f n -stabilization scheme is more sensitive to the fluctuation of f rep than f ceo -stabilization scheme. Therefore, stable f rep is still important in any sort of frequency stabilization scheme. In general, every frequency-stabilized mode-locked laser will gradually lose the frequency locking due to the long-term drift of f rep , especially when the room temperature is not rigorously regulated and the stretch length of PZT1 in Fig. 2 is limited. To keep a longer lifetime of frequency stabilization, we installed a particular-designed cooling base for controlling the cavity length in the long term, as depicted in Fig. 3a. The cooling base was connected to a chiller keeping the circulated water at (19 ± 0.05 ◦ C). Square-like partitions reduced the global turbulence during water flow. In Fig. 3b, the up-

Scan of the absolute frequency

As alluded to in Sect. 2.1, we implemented a doublepass AOM (DPA) system to retrieve the cesium spectrum and to move laser modes linearly and homogenously, as illustrated in Fig. 4. For retrieving the cesium spectrum, we applied a 35 kHz frequency dither on the DPA system. The resultant firstderivative spectrum is presented in the “Cs spectrometer” part of Fig. 1, which was obtained with a 1 MHz-span frequency dither. This approach benefited from an un-modulated radiation ( f DL ) for monitoring the absolute frequency of the modelocked pulse. To investigate the frequency accuracy, we built up a second cesium two-photon stabilized diode laser system (CTS2) without double-pass AOM and directly modulated the diode current to retrieve the cesium spectrum. We alternated between the aforementioned two different sorts of modulations and monitored the beat note between two CTS lasers; no obvious discrepancy was observed within a 300 Hz uncertainty. Once the beat note frequency between the femtosecond laser and diode laser f b (= | f n − f DL |) was stabilized, we were able to linearly scan the DPA drive frequency to move all laser modes together. Consequently, laser modes could be

FIGURE 4 Frequency tuning, modulation and stabilization of double-pass AOM (DPA) system. FG – function generator which the output frequency could either be fixed at 72 MHz or be linearly scanned; f n – absolute frequency of the nth comb mode; VCO – voltage controlled oscillator; AMP – amplifier; FC – frequency counter; PS – prescaler; DBM – double balance mixer; FL – feedback loop

CHENG et al.


Absolute frequency of f n (MHz)a f n instability (∆ f n ) Estimated accuracyb User available comb power Repetition rate instability (∆ f rep ) ac stark shift of reference laser Pressure shift of reference laserc

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364 507 094.417(15), linear scan range: 1/2 f rep 200 Hz at 100 s 3000 Hz 440 mW at 822 nm 8 mHz at 0.2 s ( f rep tunable, 80–100 MHz) −18.9 Hz/(mW/mm2 ) −386 Hz/◦ C

a

f n stands for the nth mode that was phase locked to the reference laser, value adopted from [11] with DPA frequency equals to half of S1 frequency, see Fig. 1 and text; b See text; TABLE 1 c Slope averaging from 68 to 84 ◦ C cold finger temperature system

FIGURE 5 Frequency comparison between the comb laser and the other independent cesium-stabilized diode lasers. * – Data obtained from direct diode current dither while the other data were obtained from DPA dither

scanned over the entire laser emission spectra, with fixed repetition rate. When the DPA drive frequency was fixed to half of that in the S2 synthesizer in Fig. 1, the frequency of one particular mode ( f n ) of mode-locked laser was exactly the same as the frequency of the cesium TPT-stabilized diode laser. In regard to the instability of the AOM drive frequency, we phase locked a voltage control oscillator (VCO) with an Agilent 33250A function generator (FG) as the AOM driving source, thus the instability of AOM drive frequency was reduced from ∆ f DPA = 2.6 kHz (10 s) to ∆ f DPA = 0.8 mHz (10 s). 3

Comb laser stability and accuracy

The frequency instability ∆ f comb of our comb laser system hence was analyzed as: ∆ f comb = ∆ f DL + ∆ f b ,

where ∆ f DPA is negligible as mentioned earlier, and ∆ f DL stands for the frequency instability of CTS diode laser system, that is, ∆ f DL = 150 Hz at 100 s, as had been proved in reference [14]; ∆ f b stands for the frequency instability of f b (= | f n − f DL |), that is, ∆ f b = 140 Hz at 100 s, as deduced from the bottom right part of Fig. 2. Therefore, the frequency instability of our comb laser (∆ f comb ) was estimated as ∆ f ∼ 200 Hz at 100 s. The spectral properties of the referring transition center were important in estimating the frequency accuracy of our comb laser. The power shift of atomic cesium 6S → 8S hyperfine transition is −18.9 Hz/(mW/mm2 ) and the pressure shift was smaller than 5 Hz if the cold finger tem-

Specifications of our comb laser

perature of cesium cell could be controlled to be smaller than 85 ◦ C and within 0.01 ◦ C accuracy. We estimated the accuracy of the comb frequency by the frequency comparison with the other CTS diode laser (CTS2) located on the other optical table with a different set of electronics. We turned off all lasers and the corresponding electronics after each measurement. Figure 5 shows the frequency discrepancy during 20 days of measurements which implied around 3 kHz accuracy. Uncertainty of the accuracy was attributed to the unstable room temperature during the data acquisition time period. In the accuracy measurements, two CTS diode lasers worked under the same cesium cell conditions, namely, 770 mW/mm2 power density in the cell center (the waist) and 70 ◦ C cold finger temperature. Table one summarizes the specifications of our comb laser system. 4

Conclusions

We have successfully built up a femtosecond Ti:sapphire comb laser based on a cesium-stabilized 822.5 nm diode laser. The available comb laser power was optimized and comb frequencies could be long range tuned with the repetition rate fixed, allowing for some applications of direct frequency comb spectroscopy (DFCS). We also demonstrated a novel idea of scanning and stabilizing the absolute frequency ( f n ) by shifting the pump beam horizontally, without disturbing the repetition rate ( frep ) locking. Our comb laser system is a first step towards the experiments of direct frequency comb spectroscopy (DFCS). Since we are able to monitor and dither the absolute frequency of the comb laser, we are currently working on verifying the theory of reference [19] in which the non-relevance of absolute frequency in the experiment of coherent population trap (CPT), by pulse laser is detailed. To fulfill the experiment, the repetition rate should be always kept at the integer ratio of clock transition (9.192632 GHz) while the absolute frequencies of modelocked laser were allowed to be scanned or dithered. Though we have estimated the frequency accuracy of our comb laser, the comb laser in this report is not good enough for some ultrahigh-precision frequency measurements due to the imprecision of the absolute frequency in Table 1. Therefore, the other task for future work is to improve the absolute frequency measurement on the Cs-stabilized diode laser. ACKNOWLEDGEMENTS We are grateful to Mr. Peter Chu for helping us design the cooling base of comb laser system; and the kind help of Dr. Barnes Keith in amending this article. This research is funded by the National Science Council: NSC 94-2112-M-001-022-MY3.

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Applied Physics B – Lasers and Optics REFERENCES

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